# Conjuring the Mystic Tower: amount of stone

Hi Folks!

I'm having some trouble with the amount of stone created by the spell Conjuring the Mystic Tower CrTe 35 [ArM5 p. 153]

The spell parameters are "Base 3: Create stone" with a "+4 size" adjustment. As a base individual is a single cubic pace of stone, the spell creates 10,000 cubic paces. As a pace in Ars Magica is equal to 3 feet (see this thread [url]https://forum.atlas-games.com/t/a-pathetic-newbies-spell-design-question-targets-and-sizes/4770/1]), a cubic pace is equal to 27 cubic feet. Therefore, the amount of stone created is equal to 270,000 cubic feet.

Now, the spell description speaks of a tower standing 80 feet high, 30 feet wide with a foundation of 20 feet into the ground. Assuming a rectangular shape, the volume is equal to 100 x 30 x 30 = 90,000 cubic feet. Assuming a cylinder shape with a diameter of 30 feet, the volume is equal to Pi x 15^2 x 100 = 70,000 (approximately).

That's very far from the 270,000 cubic feet...

Any thoughts ?

Nicolas

1 Like

I believe this has been recognized before, and the answer seems to be that the spell is just not "optimal" - it is designed to create the tower the wizard wants, not the largest tower that it can at that spell level. Since every magnitude adds x10 to the volume, a spell with a +3 size adjustment would only produce 27,000 cubic feet, which is not enough to create the 70,000-90,000 cubic feet tower - so you need the +4 size adjustment to create the desired tower. Theoretically a spell of the same level can be created that will create a larger tower, but a nice touch is to assert Hermetic traditionalism - this is the spell the ancients used, and that's good enough for me!

1 Like

Yeah, this spell is problematic.

It's even worse than you think. You've calculated the volume of the towers as if they are solid objects, which of course, they are not.

I don't have time to do the calculations, but I think the correct way to do it is to take your volume and subtract the volume of a smaller solid tower, say 12' radius, to account for an average three foot thickness of the walls. They are probably thicker at the foundation and not as thick at the top, and to add the volume for the floors, roof, and stairs.

2 Likes

I know, it was just to illustrate my point with a simple calculation.

Actually I did this 'cause our Bonisagus needs to know how much stone will be needed before he starts inventing the spell.

What makes me think: how wide were walls in the Middle Ages (i.e. walls of a castle, a tower, ...) ? Three feet seems a bit thin to me.

1 Like

The tower is a single stone with a volume of 90,000 cubic feet, with voids (i.e. rooms). A size +3 spell would be too small, therefore you need a size +4 spell.

A size +4 spell could be used to build a bigger tower, but this spell isn't used to build a bigger tower.

It seems plausible to argue that if the tower has voids in it, that you only need to build the substrate around the voids, and therefore only need the spell to create the actual volume of stone rather than the volume of the tower itself. Which means you can get away with a smaller size modifier. Which means you basically have two options:

• Heremtic magic is magic not engineering. Although a RL engineer might think like this, Hermetic magic is sized around the volume of the created object, rather than the mass of material within the object.
• You are right, there is a better way to make this spell. Your character can make it, and claim the kudos for doing so and providing a lab text to Durenmar, or whatever.

So it's either just a fact that Hermetic magic doesn't work like engineering, or its an opportunity for the characters in your saga to do something. Either seems fine to me, it's up to your troupe to decide which works best for them.

1 Like

I've been to ChĂ˘teau d'Angers, ChĂ˘teau de Chinon, ChĂ˘teau de Saumur, among others in France and none of those tower walls were much thicker than three feet. Castle walls were thicker, but they were made of a relatively thin layer of stone on the outside with fill in the middle. The walls of the towers were all solid rock. It would be pretty tough to make a tower with walls thicker than three feet or so. Maybe the fancy English castles did that, I don't know.

In any event, I calculate the volume of a 100 foot tower (80' above, 20' below ground) with a 15 foot radius and walls three feet thick at just over 25,000 cubic feet of stone. Throw in some stone for stairs and floors, and it's pretty close to the 27,000 that a +3 magnitude gets you.

1 Like

The Tower of Bonisagus , GotF , page 52

Standard Hermetic Laboratory & Sanctum , page 105 , Covenants
page 106

If you make the walls 1.5 feet thick , giving a radius of 13.5 feet ,
floor space is 572 sq ft (rd).
Roof and floors 1 foot thick , with 9 floors of 10 foot height.
No allowance for windows , doors or stairs ,
but hey, we have chamber of spring breezes for that sort of thing.

1 Like

Some points :

Its the traditional spell, the one that bonisagus used so it's the proper way to do it.

Medieval towers due to sheer mechanical strains usually are conical in shape (wider and the bottom than the top AND due to the way physics work, the lower you are in the tower the thicker the walls have to be just to bear the weight of what is above.

This castle has a perfect example of an old medieval donjon : chateaudemontrottier.com/
If you check this web site, English then Tour section, you will see on the bottom left a picture of the actual donjon.

Historically this castle was built at the end of the 10th century . On the same picture showing the keep, the first building to be built is, if i'm not mistaken, the one on the left. It did not even have a door on the first floor, when people wanted to enter it they climbed a ladder, which was then brought inside the castle. If someone was in, there was no way to climb to the door. Then the other parts, including the Keep, were built. Well that's what I remember from the guided tour.

(a source says : built by the Abbaye de Savigny, thus the religious usage and name of the first building).

That castle's donjon is conical, that is base is wider than the top, the hallway to enter it is on the second floor (something like 6 meters above ground) and is less than 2 feet wide. The visit is actually forbidden to overweight people. When you do visit it, everyone goes up, then everyone goes down at the same time. You can't cross inside the stairway, it's too tight.

Some numbers : 30.6 meters wide at the bottom, 33.5 meters high... That's a lot of stone. It was probably built during the 13th century, my memory of the tour is a bit fuzzy.

To come back to the spell : in my opinion, the bonisagus tower does not have to follow medieval architecture rules. There is a simple reason to that : it is created as it is instantly, thus it avoids the complication of having to build it over 10 or 15 years, just because you have to bring those 27000 cubic feet of stones where you want your donjon to be... And also, the magic knows statics, thus a "perfect" building could be built by the magic of the spell, allowing a building having lines closer to the 20th century than suspension of disbelief would bring us to think of.

(I don't know the english term for Statique, I tried statics, but it sounds weird and wrong)

I think that this spell creates a round stone building, which follows modern rules of construction, as the statics are perfectly defined (unless the spellcasting is botched of course). The main material is PERFECT stone, without cement or cracks, even though it appears to have cement and cracks from the outside (remember a craftman has to make a stonemasonry check vs finesse to detect it is made by magic). Thus as it is perfect stone, it is also perfectly balanced, allowing THIN walls. I even allow stone ducts to allow air flow between floors. At least that's how I see it. Magic is not engineering, the fact that the creator of this spell knew Stone through his mastery of Terram allowed him to break the limits of the time and build something which his cotemporary architects could not even imagine.

That's of course if in MY game

1 Like

"Statics" is indeed the right word.

Scott

1 Like

If I remember well David said the spell should be on higher level like the traditional 35 and the math is only serves this purpose.
I tend to agree with him.

1 Like